Multivariable And Parametric Functions

## Description

Suppose we wanted to turn the multivariable function,

(1)\begin{equation} f(x, y) = (x^4 - 5x^2 + 4 + y^2)^2 \end{equation}

into a parametric function, where

(2)\begin{equation} x = f(t) = 2t + 5 \end{equation}

and

(3)\begin{equation} y = g(t) = 3t - 1 \end{equation}

We can use Sage to accomplish this.

## Sage Cell

#### Code

```
var('y t')
f(x, y) = (x^4 - 5*x^2 + 4 + y^2)^2
f(x=2*t+5, y=3*t-1)
```

## Options

#### Expanding the output

The above cell produces a correct, but not easily readable output. We can clean it up with `.expand()`

#### Code

```
var('y t')
f(x, y) = (x^4 - 5*x^2 + 4 + y^2)^2
f(x=2*t+5, y=3*t-1).expand()
```

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Date: 04 Mar 2019 16:24

Submitted by: Zane Corbiere